A membrane distillation module is provided with a thin, flexible microporous membrane positioned against an impermeable condensor sheet that is stiffer in bending than the membrane. Distillate vapor diffuses through the membrane from the hot feed flowing rapidly past the membrane, and condenses and collects between, and in intimate contact with, the membrane and the condensor sheet. The condensed distillate is stripped by forces exerted by the hot feed acting on the distillate across the membrane, and flows toward a distillate outlet located in the downstream direction of the hot feed flow. Cold feed flows past the condensor sheet in the counter direction to that of the hot feed for absorbing the latent heat of condensation, and is subsequently additionally heated and introduced into the hot feed channel. Expanded microporous polytetrafluoroethylene (PTFE) is the preferred membrane material, and a spiral-wound assembly is the preferred configuration.